Math Test Musings

As a teacher, testing is one of my least favorite activities. It is necessary, but I can’t say I like it.

I recognize the advantages of testing students. First, it forces them to learn and prepare to the extent that they have to know what they are learning. They can’t rely on anyone to supply them with the knowledge they need when they have to do perform on their own.

Second, it does give me the opportunity to check whether my subjective impressions of how well the students are doing matches with actual student achievement.

Third, testing also gives me an opportunity to probe every student for misunderstandings that are tripping them up in a minimal amount of time.

As a teacher, I want to test in ways that give students credit for what they know and do correctly even if they fail to arrive at the correct solution.

I also want to remove barriers that prevent students from showing what they know. For example, unfamiliar test formats often trip students up. It isn’t that they don’t know how to solve the problems or that they can’t come up with an acceptable answer, but the format confuses them and they don’t make the right response. These are the types of barriers that make standardized testing mostly useless in providing any meaningful results.

These days, I use an online platform for testing that my district’s curriculum provides. There are limitations to the platform, but it does give a means for giving a fair test that aligns with historical classroom practices. The format provides the needed challenge for performance, but it enables me to prepare the students by utilizing the same platform for providing a study assignment. I have found that high school freshmen do not know how to study for tests. I can tell them, but it is frustrating because they often do not understand what they should do. Having them do an actual preparation assignment takes them through the practices they should employ to study for the test. Since I began doing this, test scores have been much better.

If I was a lazy teacher, I would rejoice that the online platform scores the responses for me. I could use the percent that’s correct as the grade. But then I am not really testing for student understanding. All I’m doing is yielding my professional judgment to a dumb computer. All the grade records is how well the student provided answers that matched exactly what the computer is looking for.

That is why I require my students to work their problems on paper before entering their responses into their computers. I then review every incorrect answer on every test, consulting the students’ work papers to see what they were trying to do and awarding credit for everything they knew and did right.

For example, if a student makes an incorrect response because of an arithmetic error, I give them most of the points for the problem because the test was checking to see if that student knew that alternate interior angles formed by parallel lines are congruent. The student knew that, set up the correct equation, but made a mistake in solving the equation.

Also, in working on a proof, I can avoid students being penalized because they misspelled a word in providing a justification for the test problem.

In terms of teacher time, it requires more than any other means of testing. But I do it because how else will I have an authentic assessment?

When it comes to annual state tests, though, this is exactly what they don’t do. The result is that state tests do not measure performance, not the performance of students, nor teachers, nor schools, nor districts. They are worthless.

All a state test tells us is how well the students navigated the test platform; that is, how good of a test-taker the students are.